sympy import symbols, Eq, solve

Define variables

n = symbols('n') nth_term = n * (n + 1) / 2

Compute the first 5 terms of the sequence

first_5_terms = [nth_term.subs(n, i) for i in range(1, 6)] first_5_termsThe first five terms of the sequence with the nth term $a_n = \frac{n(n+1)}{2}$ are:

$1, 3, 6, 10, 15$

These terms correspond to the triangular numbers.

Would you like an explanation of how these terms were derived? Let me know if you have any further questions!

Related Questions:

1. How do you derive the formula $\frac{n(n+1)}{2}$ for triangular numbers?
2. What are triangular numbers and their real-world applications?
3. Can you determine the 10th term of this sequence?
4. What is the sum of the first $n$ triangular numbers?
5. How do triangular numbers relate to Pascal's Triangle?

Tip:

Triangular numbers can also be visualized as dots arranged in the shape of a triangle. The $n$-th triangular number represents the total number of dots in a triangle with $n$ rows.